What is sweet spot really?

The sweet spot is not strictly a single spot. There are multiple locations on the blade pertaining to different types of shot that can produce the sensation of sweet spot. The most common ones are defined as the Node of Vibration, the Center of Percussion, the Maximum Apparent COR, and, ironically, the Dead Spot.

The Node of Vibration(Node)(varies but usually between B & C) generates the least feedback in the hand. The Center of Percussion(COP)(varies but generally between C & D) exerts the least torque on the wrist. The Maximum Apparent COR(ACOR) produces the best bounce(E), and lastly, the Dead Spot(A) produces the least bounce and yet couples the energy of the swing with that of the ball the best.

In simple terms:

For slow and spinny serve, kick serve, heavy push, backspin opener, fast loopkill and high smash into which you want to put the most energy of your swing, you'd aim for the dead spot. For low and short serve return, and chop where you want the blade to cancel out as much energy of the ball, you'd also aim for the tip of the blade.

For counterlooping off the table where the ball packs a punch and you'd expend a lot of energy, you'd want to hit within the Node and the COP to minimize residue vibration and torque, which potentially reduces accuracy.

For fast blocks, you'd aim for the ACOR and let the ball do the job.

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Here is modal analysis 101. An object has an infinite number of natural frequencies. With each natural frequency there is a corresponding mode shape, collectively known as the mode of vibration. The physical properties such as the mass, shape, and stiffness of an object dictate the frequencies it will vibrate at.

In modal analysis, an impact test would be performed on an object to observe its modes of vibration. The object would respond(resonate) to frequencies that correspond to its natural frequencies. The duration of impact(contact time) characterizes the frequency content of the input force. Thus, an ideal input is one that has the shortest duration, and with enough force, which would generate a constant response across the entire range. In real world tests, an impact hammer is carefully chosen to excite only the frequencies of interest in order to reduce noise.

For table tennis, the ball is the best impact hammer as it simulates real-world situations. A 1ms impact(the typical dwelltime for blade+rubbers) would excite modes below 1kHz, .5ms for those below 2kHz and so on. The wave generated by the impact would travel across and reflect within the boundaries of the blade. The lower end of the frequencies is responsible for both blade head and handle vibration and thus a lot of it would get absorbed by the hand. The upper end has more to do with just the blade head vibration and would travel away as sound.

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Other than the speed, the mode of vibration can reveal a lot about a blade.

The 1st bending mode is usually within the first few hundred Hz, lower for a clamped blade, and higher for a freely-suspended blade, with the real-world grip resembling the latter, but with higher damping.

The 1st torsional mode follows closely. The 2nd bending mode comes next, and so on. The membrane mode doesn't come in until much later.

The 1st bending mode contributes the most to dwell/feel as the handle vibrates the most at that frequency. That mode is also related to the sweet spot as one node(least vibration) is somewhere in the upper center of the blade head and another node where the handle meets the blade head.

The 1st torsional mode gets agitated the most when the racket is hit off-centered.

As the mode goes higher, the role it has in the racket-ball interaction diminishes. Looking at the data, it looks like the mic is picking up the membrane mode the most, which contributes the most to the sound of the blade.

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frankhond said:

Having tried some blades, the feeling is different. For example

• Primorac (5ply) has a small spot where the hit feels and sounds loud and clear. Moving away from this spot feels increasingly like a dead 'thunk'.
• Hadraw VK has a much larger spot where the hit sounds and feels clear, almost like a bell.
• Viscaria (5+2ALC) produces a sharp and clear crack almost over the entire blade.

I suppose this is what people refer to as a "sweet spot". But is this only a feeling issue or does this sweet spot have effect on the quality of the shot itself? I know that the smaller sweet spot teaches a beginner where to hit, but I'm interested in the physical properties. How does hitting the sweet spot affect the response of the racket, as opposed to hitting nearer the edge? Does the Viscaria produce the most "clean" shots because the sweet spot is largest?

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Below is what I've collected after The Great Brainstorming of 2012.

The dwell we feel and actual dwell time are actually related. The actual dwell time has a direct influence on the vibrations that are excited. Vibrations with a period shorter than the actual dwell time are strongly suppressed. In a way, it's like a footprint, from which you can tell a number of things about the living being that left it behind. You can't tell exactly but you get a rough idea, a ballpark figure, so to speak.

For tennis, the membrane modes(string-bed vibration) are said to have a strong influence on dwell-time and racket power, but has little to do with feel since they don't involve vibration of the handle.

For table tennis, however, the membrane modes could have an influence on feel since the thumb and index finger could touch the blade head. The frequency of the 1st membrane mode for a hand-held racket(blade+rubbers) also falls within the upper end of the Pacinian corpuscle(20-1000Hz). Therefore, there's reason to believe we could feel the membrane mode unlike other racket sports.

Unfortunately, I'm not aware of any table tennis studies or papers that look at both dwell time and the higher modes of vibration. The closest one from Taiwan looks at the dwell time and only the fundamental mode.

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